Tables of Mellin transforms

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9780387069425: Tables of Mellin transforms
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This book contains tables of integrals of the Mellin transform type z-l J (a) 1> (z) q,(x)x dx o t Since the substitution x = e- transforms (a) into (b) 1> (z) the Mellin transform is sometimes referred to as the two sided Laplace transform. The use of the Mellin transform in various problems in mathematical analysis is well established. Parti­ cularly widespread and effective is its application to problems arising in analytic number theory. This is partially due to the fact that if ¢(z) corresponding to a given q,(x) by (a) is known, then ¢(z) belonging to xaq,(x) or more general to P xaq,(x ) (p real) is likewise known. (See particularly the rules in sections 1. 1 and 2. 1 of this book. ) A list of major contributions conce~ning Mellin trans­ forms is added at the end of the introduction. Latin letters (unless otherwise stated) denote real positive numbers while Greek letters denote complex parameters within the given range of validity. The author is indebted to Mrs. Jolan Eross for her tireless effort and patience while typing this manuscript. Oregon State University Corvallis, Oregon May 1974 Fritz Oberhettinger Contents Part I. Mellin Transforms Introduction. . . · . · · · . · . . . . . . . . . . . . · · · · . . . · . · . . · · · . · . 1 Some Applications of the Mellin Transform Analysis. ··. ···. . . ·. ·. . . . ·· . · . . . . . . ··. . . . . ·· 6 1. 1 General Formulas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1. 2 Algebraic Functions and Powers of Arbitrary Order . . . 13 1. 3 Exponential Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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9783540069423: Tables of Mellin Transforms

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ISBN 10:  3540069429 ISBN 13:  9783540069423
Publisher: Springer, 1975
Softcover

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Oberhettinger, Fritz
Published by Springer-Verlag, New York (1974)
ISBN 10: 0387069429 ISBN 13: 9780387069425
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Book Description Springer-Verlag, New York, 1974. Softcover. First Edition, First Printing. Octavo; VG/no-DJ paperback; yellow spine with black text; cover has rubbing, spotting along spine, minor edgewear; textblock has staining and rubbing around edges, otherwise clean; pp 275. Full-priced Rockville. Seller Inventory # 14-116-1295636

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